Economic analysis depending on the timing. Economic analysis and its role in enterprise management

Analysis is a way of knowing objects and phenomena of the environment, based on the division of the whole into its constituent parts and the study of them in all the variety of connections and dependencies.

The analysis can be considered in two aspects:

theoretical;

and specifically economic.

Theoretical, or political-economic, analysis is predominantly a qualitative logical analysis based on a high degree of abstraction, i.e., an analysis of the operation of economic laws, categories, abstract concepts.

Specific economic analysis is primarily a quantitative analysis expressed in specific calculations and formulas.

Theoretical and concrete analysis are always interconnected. Any formula or model must be not only formally mathematically correct, but also theoretically substantiated on the merits of the phenomenon or indicator under consideration.

In addition, macroeconomic analysis and microeconomic analysis are distinguished.

Macroeconomic analysis studies economic phenomena and processes at the level of the global and national economy.

Microeconomic analysis studies economic phenomena and processes at the level of individual business entities (enterprises or organizations).

Economic analysis has developed in economic research as an independent science with its own subject and research method.

Economic analysis as a science is a system of special knowledge about the methods and techniques of research used to process and analyze economic information about the activities of enterprises.

Economic analysis as a practice is a type of management activity that precedes the adoption of management decisions and boils down to substantiating these decisions on the basis of available information.

Economic analysis and its role in enterprise management

Currently, economic analysis occupies an important place among the economic sciences. It is considered as one of the functions of production management. It is known that the management system consists of the following interrelated functions: planning, accounting, analysis and management decision making

The initial element of the management system is planning, which determines the direction and content of the activities of an economic entity. An important element of planning is the determination of ways to achieve the set goal - to achieve the best financial results.

To manage production, you need to have complete and truthful information about the progress of the production process, about the progress of the plans. Therefore, one of the functions of production management is accounting. Without reliable and complete information, it is almost impossible to make optimal management decisions. Accounting ensures constant systematization and generalization of data necessary for production management and control over the implementation of business plans.

To optimize management, it is necessary to have a clear idea of the trends and nature of changes in the economy of an economic entity. Comprehension, understanding of information is possible only on the basis of economic analysis. In the process of analysis, "raw" primary information is checked. Compliance with established forms, correctness of arithmetic calculations, reducibility and comparability of indicators are determined. Then the information is processed: there is a general familiarization with the documents and their content; deviations are determined and compared; the influence of factors on the analyzed object is determined, reserves and ways of their use are identified. Identifies shortcomings and errors. The results of the analysis are systematized and summarized. Based on the results of the analysis, management decisions are made.

It follows that economic analysis substantiates managerial decisions, ensures the objectivity and efficiency of production management.

Thus, economic analysis is an objectively necessary element of production management and is a stage of management activity. With the help of economic analysis, the essence of economic processes is known, the economic situation is assessed, production reserves are identified and scientifically based decisions are prepared for planning and management.

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Method of economic analysis

The word "method" came into our language from the Greek language. In translation, it means "the path to something." Therefore, the method is, as it were, a way to achieve the goal. As applied to any science, the method is the ϶ᴛᴏ way of studying the subject of the ϶ᴛᴏth science. The methods of any sciences in its basis have a dialectical approach to the study of the objects and phenomena they consider. The economic analysis will not be an exception here.

The dialectical approach means that all processes and phenomena taking place in nature and society should be considered in their constant development, interconnection and interdependence. So economic analysis studies the indicators characterizing the activities of any organizations, comparing them over several reporting periods (in dynamics), as well as in their change. Further. Economic analysis considers various aspects of the organization's activities in unity and interconnection, as elements of a single process. For example, the volume of sales of products depends on its output, and the fulfillment of the planned target for profit depends mainly on

The method of economic analysis is determined by its subject and the challenges ahead.

Methods and techniques, used in the analysis of economic activity, are divided into traditional, statistical and economic and mathematical. It is worth noting that they are discussed in detail in the relevant sections of the site.

In order to practically implement the use of the method of economic analysis, certain techniques have been developed. It is worth noting that they are a set of methods and techniques used to optimally solve analytical problems.

The techniques used in economic analysis at individual stages of analytical work involve the use of various techniques and methods.

The key moment of the method of economic analysis will be the calculation of the influence of individual factors on economic indicators. Relationship economic phenomena represents a joint change of two or more given phenomena. There are various forms of interconnections between economic phenomena. The most significant among them will be the causal relationship. Its essence lies essentially in the fact that a change in one economic phenomenon is caused by a change in another economic phenomenon. Such a relationship is called deterministic, otherwise - a causal relationship. If two economic phenomena are connected by such a relationship, then the economic phenomenon, the change of which causes a change in the other, is called a cause, and the phenomenon that changes under the influence of the first is called a consequence.

In economic analysis, those signs that characterize the cause are called factorial, independent. Note that the same signs, which characterize the consequence, are usually called resultant, dependent.

See next: Factor Analysis

Thus, in this paragraph, we examined the concept of the method of economic analysis, as well as the most important methods (methods, techniques) used in the analysis of the organization's activities. We will consider these methods and the procedure for their use in more detail in special sections of the site.

Tasks, sequence of conducting and procedure for processing the results of economic analysis

The most complete and deep will be the internal (on-farm) analysis carried out traditionally by the functional departments and services of this organization. Therefore, internal analysis faces much more numerous tasks than external analysis.

The main tasks of the internal analysis of the organization's activities should be considered:

verification of the validity of the tasks of business plans and various standards;
determination of the degree of fulfillment of tasks of business plans and compliance with established standards;
calculation of the influence of individual factors on the magnitude of the deviation of the actual values of economic indicators from the base ones
finding on-farm reserves to further improve the efficiency of the organization and ways to mobilize, that is, the use of these reserves;

Of the listed tasks of internal economic analysis main task will identify reserves in the organization.

Before external analysis, there is, in essence, only one task - to assess the degree of solvency and liquidity of the organization both at a certain reporting date and in the future.

The results of the analysis will be the basis for the development and implementation of optimal management decisions that help improve the efficiency of organizations.

In the process of conducting economic analysis can be used methods of induction and deduction.

Induction method(from particular to general) suggests that the study of economic phenomena begins with individual facts, situations and proceeds to the study of the economic process as a whole. Method same deduction(from general to particular) is characterized, on the contrary, by the transition from general indicators to particular ones, in particular, to the analysis of the influence of individual factors on generalizing economic indicators.

Do not forget that the deduction method will, of course, be the most important when conducting economic analysis, since the sequence of analysis usually involves the transition from the whole to its constituent elements, from synthetic, generalizing indicators of the organization's activities to analytical, factor indicators.

When an economic analysis is carried out, all aspects of the organization's activities, all the processes that make up the production and commercial cycle of the organization, are examined in their interconnection, interdependence and interdependence. Such a study is the key moment of the analysis. It is worth noting that it is called factor analysis.

After the end of the analysis, its results should be formalized in a certain way. It is worth saying that explanatory notes to annual reports, as well as certificates or conclusions based on the results of the analysis, can be used for these purposes.

Explanatory notes intended for external users of analytical information. We will study what the content of these notes should be.

They should reflect the level of development of the organization, the conditions in which its activities take place, the competitiveness of products, the pricing policy for it, data on product sales markets, etc. should also be provided. Information should also be provided on at what stage life cycle every kind of product is on the market. (They include the stages of implementation, growth and development, maturity, saturation and decline) Excluding the above, it is extremely important to provide information about the competitors of this organization.

Then, data on the main economic indicators should be presented for several periods.

Those factors that have influenced the organization's activities and its results should be indicated. one should also cite those activities that are planned to eliminate shortcomings in the activities of the organization, as well as to increase the efficiency of ϶ᴛᴏth activities. Material published on http: // site

References, as well as conclusions based on the results of the economic analysis carried out, may have more detailed content compared to explanatory notes. As a rule, references and conclusions do not contain generalized characteristics of the organization and the conditions for its functioning.
It is worth noting that the main emphasis here is on the description of reserves and ways to use them.

The results of the study can also be presented in non-textual form. In this case, the analytical documents contain only a set of analytical tables and there is no text characterizing the economic activity of the organization. By the way, this form of registration of the results of the conducted economic analysis is now being used more and more widely.

In addition to the considered forms of registration of the results of the analysis, the introduction of the most important of them into certain sections will also be applied. economic passport of the organization.

These are the main forms of generalization and presentation of the results of the economic analysis. It should be borne in mind that the presentation of the material in explanatory notes, as well as in other analytical documents, should be clear, simple and concise, and should also be linked to analytical tables.

Types of economic analysis and their role in the management of the organization

Financial and managerial economic analysis

Economic analysis can be subdivided into various types in ϲᴏᴏᴛʙᴇᴛϲᴛʙ and with certain characteristics.

First of all, economic analysis is usually divided into two main types - the financial analysis and management analysis- depending on the content of the analysis, the functions it performs and the tasks facing it.

The financial analysis, in turn can be subdivided into external and internal. The first is carried out by tax authorities, banks, statistical authorities, higher organizations, suppliers, buyers, investors, shareholders, audit firms, etc.
It should be noted that the main task of external financial analysis will be to assess the financial condition of the organization, its solvency and liquidity. It is carried out at the organization itself by the forces of its accounting department, financial department, planning department, other functional services. Internal financial analysis solves a much wider range of tasks compared to the external one. Internal analysis examines the effectiveness of the use of equity and borrowed capital, examines the indicators of profit, profitability, identifies reserves for the growth of the latter and strengthening the financial condition of the organization. Internal financial analysis, therefore, is aimed at developing and implementing optimal management decisions that contribute to improving financial indicators activities of this organization.

Management analysis, as opposed to financial is internal. It is carried out by the services and departments of this organization. It is worth noting that he studies issues related to the organizational and technical level and other conditions of production, using certain types of production resources (labor resources, fixed assets, materials), analyzes the volume of output, its cost.

Types of economic analysis depending on the functions and tasks of the analysis

Taking into account the dependence on the content, functions and tasks of analysis, the following types of analysis are also distinguished: socio-economic, economic-statistical, economic-environmental, marketing, investment, functional-cost (FSA), etc.

Socio-economic analysis examines the relationship and interdependence between social and economic phenomena.

Economic and statistical analysis used to study mass socio-economic phenomena. Economic-ecological analysis studies the relationship and interaction between the state of ecology and economic phenomena.

Marketing Analysis has as its goal the study of the markets for raw materials and materials, as well as the markets for finished products, the balance of supply and demand for these products, the competitiveness of the products of this organization, the level of prices for products, etc.

Investment analysis aimed at choosing the most effective options investment activity organizations.

Functional cost analysis(FSA) is a method of systematic study of the functions of a product, or any production and economic process, or a certain level of management. This method has the goal of minimizing the cost of designing, launching production, selling products, as well as industrial and domestic consumption of these products under conditions of their high quality, maximum usefulness (including durability)

Given the dependence on aspects of the study, there are two main types (directions) of analysis of economic activity:

financial and economic analysis;
technical and economic analysis.

The first type of analysis studies the influence of economic factors on the implementation of business plans in terms of financial indicators.

Note that the technical and economic analysis examines the impact on the economic performance of the factors of engineering, technology and organization of production.

Given the dependence on the completeness of coverage of the organization's activities, two types of analysis of economic activity can be distinguished: full (complex) and thematic (partial) analysis. The first type of analysis covers all aspects of the financial and economic activities of the organization. Note that thematic analysis studies the effectiveness of certain aspects of the organization's activities. Economic analysis can also be divided according to the objects of study. Microeconomic and macroeconomic analysis. Microeconomic analysis studies the activities of individual economic units. It can be divided into three main types: intrashop, shop and factory analysis.

Macroeconomic, it can be sectoral, that is, study the functioning of a particular sector of the economy or industry, territorial, which analyzes the economy of individual regions, and, finally, intersectoral, examining the functioning of the economy as a whole.

a separate feature classification of types of economic analysis will be a division of the latter by subjects of analysis. They are understood as those bodies and persons who carry out the analysis.

The subjects of economic analysis can be divided into two groups.

Directly interested in the activities of the organization. The ϶ᴛᴏth group may include the owners of the organization's funds, tax authorities, banks, suppliers, buyers, management of the organization, individual functional services of the analyzed organization.
Subjects of analysis indirectly interested in the activities of the organization. This includes legal organizations, audit firms, consulting firms, trade union bodies, etc.

Economic analysis depending on the timing

Given the dependence on the time of the analysis (in other words, on the frequency of its implementation), there are: preliminary, operational, final and prospective analysis.

preliminary analysis allows you to assess the state of this object when developing a business plan. For example, the production capacity of the organization is assessed, whether it is able to provide the planned volume of production.

Operational(otherwise current) analysis is carried out on a daily basis, directly in the course of the current activities of the organization.

final(subsequent, or retrospective) analysis examines the effectiveness of the economic activities of organizations for the past period.

Perspective analysis is used to determine the expected results in the coming period.

Forward-looking analysis is critical to ensure the success of the organization in the future. This type of analysis examines possible options development of the organization and outlines ways to achieve optimal results.

Types of economic analysis depending on the research methodology

Considering the dependence on the methodology used for studying objects in the economic literature, it is customary to subdivide the analysis of economic activity into the following types: quantitative, qualitative, express analysis, fundamental, marginal, economic and mathematical.

Quantitative(otherwise factorial) analysis is based on quantitative comparisons, measurement, comparison of indicators and the study of the influence of individual factors on economic indicators.

Qualitative Analysis uses qualitative comparative assessments, characteristics, as well as expert assessments of the analyzed economic phenomena.

Express analysis- ϶ᴛᴏ a way to assess the economic and financial condition of an organization on the basis of certain signs expressing certain economic phenomena. Fundamental analysis is based on a comprehensive, detailed study of economic phenomena, traditionally based on the use of economic-statistical and economic-mathematical research methods.

Margin Analysis explores ways to optimize the amount of profit received as a result of sales of products, works, services. Economic and mathematical analysis is based on the use of a complex mathematical apparatus, with the help of which it is established best option solutions to any economic mathematical model.

Dynamic and static economic analysis

According to its nature, economic analysis can be divided into two following: dynamic and static. The first type of analysis is based on the study of economic indicators taken in their dynamics, that is, in the process of their change, development over time, for several reporting periods. In the process of dynamic analysis, indicators of absolute growth, growth rate, growth rate, absolute value of one percent growth are determined and analyzed, and dynamic series are constructed and analyzed. Static analysis assumes that the studied economic indicators will be static, that is, unchanged.

According to the spatial basis, economic analysis can be divided into the following two types: internal (on-farm) and inter-farm (comparative). The first one studies the activities of this organization and its structural divisions. In the second type, the economic indicators of two or more organizations are compared (the analyzed organization with others)

According to the methods of studying the object of analysis, it is divided into the following types: complex, system analysis, continuous analysis, selective analysis, correlation analysis, regression analysis, etc. Do not forget that essential has a comprehensive final analysis of the activities of organizations, comprehensively studying their work for the reporting period; the results of the ϶ᴛᴏth analysis can be used for both short-term and long-term forecasting.

Operational economic analysis

Operational economic analysis applied at all levels of government. The share of operational analysis in making optimal management decisions increases with approach to individual organizations and their structural divisions.

Do not forget that the most important feature of operational analysis will be that it is as close as possible in time to the implementation of individual phases of the production and commercial cycle of a given organization. operational analysis timely establishes the causes of existing shortcomings and their perpetrators, reveals reserves and promotes their temporary use.

Final economic analysis

A very important role in the development of optimal management decisions is played by final, subsequent analysis. Do not forget that the most important source of information for such an analysis will be the reporting of the organization.

Final Analysis gives a refined assessment of the organization's activities and its results for a certain period, ensures the identification of reasonable values of reserves to increase the efficiency of the organization's activities, seeks ways to mobilize, that is, use these reserves. The results of the final analysis carried out by the organization itself are reflected in explanatory note to the annual report.

The final analysis will be the most complete type of analysis of the economic activities of the organization.

The method of economic analysis is usually understood as a dialectical approach to the study of economic processes in their formation and development. A feature of the method of economic analysis is that it uses a system of indicators that at various levels of management most widely characterize the subject of market relations, reveals and measures the tightness of the relationship of these indicators. The need for such an approach is due to the fact that the study of each indicator in isolation from others generates erroneous conclusions, making it difficult to understand the underlying processes taking place in the organization, the choice of measures necessary to improve economic activity.

Proceeding from this, the method of economic analysis is a set of techniques and methods for studying the economic activity of enterprises by identifying and determining the relationships of the studied indicators, dividing them into components and comparing them with others, measuring the magnitude of the influence on the studied indicators of both individual components and their combination in unity and mutual connection.

At the initial stage of the analysis of one or another indicator, the study is carried out from the general to the particular, which is a deductive method of research. At the stage of generalization, the studied components of the analyzed indicator are considered taking into account their influence on the general analyzed indicators, which is an inductive method of research. Deductive and inductive methods of research are two sides of the process of studying phenomena. This shows the unity and inextricable link between analysis and synthesis. The application of each element of the method is achieved by a combination of techniques and methods of economic analysis.

In the process of economic analysis, analytical processing economic information a number of special methods and techniques are used.

Exists different classification methods and techniques of economic analysis, depending on the characteristics under study.

Methods and techniques of economic analysis can be divided into two groups: formalized and non-formalized.

Formalized methods make it possible to present indicators in strict dependence (mainly mathematical). Among them are:

classical methods of economic analysis;
factor analysis methods;
economic and mathematical methods;
graphic method, etc.

The classical methods and techniques of economic analysis include: the method of absolute, relative values and average values, the method of comparing indicators; grouping; drawing up analytical tables, etc.

Among the methods of factor analysis, one can single out the index method; elimination techniques (method of absolute and relative differences, method of chain substitution), balance method.

The economic and mathematical methods widely used in economic analysis include the method of correlation and regression analysis, cluster analysis, econometric methods, mathematical programming methods, game theory, queuing theory, inventory optimization method (Wilson model), etc.

The graphical reflection of the results is their representation on graphs using various geometric shapes, lines, points - the most visual way to display and characterize the analyzed data. In economic analysis, two main types of graphs are used - diagrams and cartograms.

In diagrams, reporting data is displayed in the form of various figures and lines, and in cartograms - in the form of symbols on the diagrams. Depending on the construction method, there are bar, sector (pie), line and curly charts.

Non-formalized methods are based on reflection analytical procedures at the logical level, and not on strict analytical dependencies. These include the development of a system of indicators, the method of expert assessments, the methods of situational analysis, SWOT analysis, PEST analysis, the method of functional cost analysis, the method of marginal analysis, etc.

Classical methods of economic analysis

In each case, the comparison depends on the purpose of the analysis and the tasks facing it.

Consider the most typical situations in which the comparison method is used.

1. Identification of the degree of implementation of plans by comparing the relevant actual indicators with the planned ones (Table 12.1).

Table 12.1

As can be seen from Table. 12.1, the profit plan was fulfilled by 105.8%, 661 thousand rubles were received in excess of the plan. arrived. At the same time, the plan for the sale of products is underfulfilled by 0.8% (99.2 - 100.0). AT reporting year products were sold for 824 thousand rubles. less than planned.

2. Comparison of the actual indicators of the reporting period with the corresponding indicators of the previous (past or base) period (Table 12.2).

Table 12.2

The data in Table 12.2 allow us to draw the following conclusions. AT reporting period the organization produced products A more than in the base period by 16 units, or 4.9%. The production of products B decreased by 18 units, or 4.2% (95.8 - 100.0) compared to the base period.

3. Comparison of the actual indicators of the reporting period with the average values of these indicators for the past three to five years (Table 12.3).

Table 12.3

The data in Table 12.3 indicate that the sales of products A are developing successfully, since in the reporting year, sales exceeded not only last year, but also the average annual level. The sale of product B requires a deeper study, since in the reporting year the sales volume was not only less than last year, but less than the average annual sales over the past five years.

4. The assessment of reserves for increasing production is carried out by comparing the actual data on the volume of production for the reporting year with the planned indicators determined taking into account organizational and technical measures to increase production.

5. Comparison of some economic indicators with other indicators of the organization's activities (Table 12.4).

Table 12.4

As can be seen from the data in Table. 12.4, the financial condition of the organization has deteriorated somewhat, as the duration of receivables has increased, and accounts payable has decreased. This may mean that the organization has had difficulties with the sale of products (for example, due to a decrease in demand) and is forced to increase the term of commercial credit for buyers. At the same time, the duration of accounts payable has increased, which may indicate a decrease in supplier confidence in the organization. Comparing the change in the ratio of the turnover of receivables and payables, we can come to the same conclusions, since it has increased in dynamics.

A prerequisite for applying the comparison method should be the comparability of the compared indicators (planned and reporting indicators, indicators of the reporting and past periods, etc.), which implies:

comparability of volume, cost, quality, structural indicators;
the unity of the time periods for which the comparison is made;
comparability of production conditions;
comparability of the methodology for calculating indicators.

We emphasize that only qualitatively homogeneous quantities can be compared.

The identified deviations are the object of further analysis. When analyzing deviations from planned values, it is advisable to assess the quality of the planning itself. So, for example, significant positive deviations from the plan (overfulfillment of the plan) may be the result of an underestimated or insufficiently stressed plan.

Grouping of analytical information is the division of the studied set of objects into homogeneous groups according to the corresponding characteristics. This method of analysis is often an integral part of the analytical study. A simple calculation of the results, comparison of indicators does not always allow a sufficiently complete assessment of the characteristics of the organization's activities, the dynamics of its indicators. Therefore, prior to the implementation of the calculations, a preliminary characterization of the population, its grouping, is carried out. It allows you to study economic phenomena and processes in interconnection, interdependence, identify the most significant factors, discover certain trends and patterns inherent in these phenomena and processes. Groupings of initial data are widely used in the analysis of planned and reporting indicators. With their help, you can show the dependence of the level of costs on the volume of sales, turnover, etc. Without grouping, it is impossible to find out why the plan was overfulfilled or underfulfilled, how it is carried out different types organizations.

The objects of study are both the economic entities themselves and their structural units, business operations.

Grouping involves the classification of phenomena and processes, as well as the causes and factors that determine them. It is impossible to group phenomena according to a random sign; it is necessary to make a reasonable choice of signs. One of the most important methodological principles underlying the scientific choice of grouping characteristics and the construction of groupings is the provision according to which they should be produced with the obligatory consideration of the qualitative characteristics of the grouped units of the population. These characteristics should take into account the essential (most important) features of the phenomenon, process or object being studied, making it possible to unite units of the studied population that are homogeneous in terms of socio-economic and legal nature into separate (independent) groups. Only thoughtful groupings make it possible to deeply analyze the phenomena, characterize their features, the relationship between individual indicators.

Groupings are divided according to the complexity of construction:

simple (with the help of which the relationship between objects structured according to a certain attribute is studied);
combined (first they are divided according to one attribute, and then within each subgroup there is a division according to other attributes).

Depending on the goals of the analysis, typological, structural and analytical groupings are used.

In economic analysis, structural groupings are widely used in the study of the composition of economic entities (but the power, the level of automation, the value of fixed assets, etc.).

Typological groupings make it possible to delimit the studied populations into homogeneous groups, types according to an essential qualitative feature. An example of a typological grouping can be a grouping of organizations by type of activity or by form of ownership. The typological grouping is drawn up in a table, the selected groups (based on a combination of grouping characteristics) are combined into the intended types, and the number is determined ( specific gravity) of each of them.

Structural grouping of analytical information can be carried out in order to study the change in the structure of typically homogeneous groups of phenomena, processes or objects. For a structural grouping, it is necessary to have homogeneous aggregates, divided according to the size of the changing attribute. If the typological grouping is based on qualitative features, then the structural grouping is based on the quantitative features of the studied population. Structural groupings allow you to study the internal structure of the indicator and the ratio of its individual parts. For example, with the help of structural grouping, you can study the composition of products by product range and assortment, the composition of workers by profession, length of service, by age, etc. In the process of analytical work, it is possible to group organizational units according to the level of implementation of the plan, labor productivity, equipment loading, equipment with means of automation and mechanization of labor, etc., in order to determine the level of economic efficiency of individual organizational units, to identify reserves for improving the work of lagging units.

Analytical groupings are distribution according to dependence, the relationship between two or more heterogeneous groups of phenomena or their features. Analytical groupings make it possible to identify interrelations, interdependencies and interactions of the studied indicators, phenomena, objects. They make it possible to identify many hidden dependencies and relationships, which is important for making managerial decisions and developing the economic activity of the organization. For example, when studying customer demand for an organization's products, it is advisable to group customers by gender, age, income level, place of residence, and other characteristics.

Ways of tabular reflection of analytical data are the most rational and easy-to-perceive forms of presenting the results of analysis.

The results of the analytical summary and grouping, as a rule, are placed in analytical tables, which are a rational, visual, compact and systematized presentation of the indicators studied in the process of economic analysis.

The horizontal lines of a table are called rows, and the vertical lines are called graphs (columns, columns). Each row and column has its own name (heading), the corresponding content of the indicators placed in the table, and the table as a whole has a common name that determines its content.

Any correctly compiled table contains two main elements: the subject and the predicate. The subject is an object of study or a list of units of the population (their groups), which are characterized in the table. The predicate is a list of indicators that characterize the subject.

When developing analytical tables in the process of summarizing and grouping indicators used for analysis, it should be borne in mind that the table should not be a simple summary of data placed in an arbitrary order. Each table should contain an analytical presentation of the results of the observation, so that a digital picture of the phenomena that are to be analyzed is developed in a sequential series of lines and graphs.

The table should be optimal in size. On the one hand, it should contain all the necessary indicators, on the other hand, it should not be overloaded with redundant statistical information.

The table should have a clear common title, as well as the names of the subject and predicate, their groups and sections. Tables without titles are difficult to understand. In addition, they must indicate the units of measurement, territory, time period and other necessary information, binding the table to a specific content, amount of data, time and space.

Subject lines and predicate columns can be placed from particular to general or vice versa. Totals are usually placed on the last line or column. However, based on the tasks solved by the table, the totals can be given in the first line.

If the table is large, its rows and columns can be numbered (designated) by ordinal numbers or alphabetical letters.

All numerical data given in the table must have the same degree of accuracy (whole numbers, integers with tenths or hundredths), which facilitates the perception of the information contained in the table.

In the absence of data for a certain year or for some parameter, an ellipsis or “no data” is usually put instead of the corresponding figures. If the absence of some data is an objective fact (for example, the absence of a change in any indicator), then a dash (dash) is put instead of the corresponding data.

All doubts and questions that may arise when reading the table should be disclosed in the notes to it.

Methods of functional factor analysis

An important component of economic analysis is the study and quantitative assessment of the influence of factors on the value of the studied economic indicators.

Economic factor analysis is understood as the disclosure of a full set of direct, quantitatively measurable factors that influence the change in the performance indicator and the assessment of their impact.

According to the nature of the relationship between the indicators, the methods of functional (deterministic) and stochastic factor analysis are distinguished.

Deterministic (functional) factor analysis is a technique for studying the influence of factors, the relationship of which with the performance indicator is of a functional nature.

The main differences of this method of analysis are:

building a deterministic model based on logical analysis;
the presence of a direct or inverse functional relationship between factor and performance indicators;
the impossibility of separating the results of the influence of simultaneously acting factors that cannot be combined in one model;
study of interrelations in the short term.

The disadvantage of deterministic factor analysis is that the scientific and technical factors of production intensification cannot be included in the model of direct links, and therefore, their underestimation will lead to underestimation or overestimation of individual results. Another disadvantage is that the results of the calculations will depend on how logically and economically sound the dependency model is, and on this, in turn, the conclusions depend.

There are four types of deterministic models:

multiplicative;
additive;
multiples;
mixed.

Multiplicative models in a generalized form can be represented by the formula

where Y is the performance indicator; Σ is the sum factor indicators; x 1 , x 2 , ..., x n are the factors whose influence is studied in this model.

Such models, for example, include the proceeds from the sale of the organization's products as the sum of sales of certain types of products, the amount as the sum of conditionally constant and conditionally variable cost items, etc.

Multiple models are the ratio of factor indicators and have the form:

where B is the proceeds from the sale of goods for the period under study; W is the average stock of goods.

Mixed (combined) models are a combination of the above models and can be described using special expressions:

Examples of such models are indicators of capital costs per 1 ruble. manufactured products, profitability indicators, etc.

For a deeper study of the relationship between indicators and the quantitative measurement of many factors that influenced the performance indicator, you can use model transformations to include new factor indicators.

To detail the generalizing factor indicator into its components, which are of interest for analytical calculations, use the method of lengthening, expanding, reducing the factor system (these methods are discussed in paragraph 10.6).

The detail of factor analysis is largely determined by the number of factors whose influence can be quantified, so multifactor models are of great importance in the analysis. They are based on the following principles:

the place of each factor in the model should correspond to its role in the formation of the effective indicator;
the model should be built from a complete two-factor model by sequentially dividing the factors, usually qualitative ones, into components;
when writing a multivariate model formula, the factors should be arranged from left to right in the order of their replacement.

Building a factor model is the first step in deterministic analysis. Next, a method for assessing the influence of factors is determined.

The index method is based on relative indicators expressing the ratio of the level of a given phenomenon to its level taken as the basis for comparison (to its level in the past or to the level of a similar phenomenon taken as a base).

Several types of indices are used in the analysis: aggregate, arithmetic, harmonic, etc. Allocate individual and aggregate (group) indices. Indexes expressing the ratio of directly commensurate quantities are called individual, and those characterizing the ratio of complex phenomena are called aggregate (group). Individual indices are calculated by indicators, but which are not factorial models. For example, price (p), cost (c), volume (q).

This method is used in multiplicative and multiple models.

Using the aggregate formula of indices and following the established computational procedure, it is possible to determine the influence of factors on the change in the effective indicator. The calculation algorithm is as follows:

Σx 1 y 1 - Σx 0 y 0 = (Σx 1 y 1 - Σx 0 y 1) + (Σx 0 y 1 - Σx 0 y 0)

where x is a quantitative factor; y is a qualitative factor; J xy \u003d Σx 1 y 1 / Σx 0 y 0 - index of change in the resulting indicator; J x = Σx 1 y 0 / Σx 0 y 0 is the influence of the quantitative factor; J y = Σx 0 y 1 / Σx 0 y 0 - influence of the qualitative factor.

By calculating the indices and constructing a time series that characterizes, for example, output in value terms, one can judge the dynamics of production volume in a qualified manner.

Example 12.1

The turnover of the trade organization in the reporting year amounted to 78,300 thousand rubles, in the past - 64,100 thousand rubles. Prices in the reporting year increased by an average of 18%. It is necessary to determine:

change in the value of turnover in the reporting year;
influence on the change in the turnover of the price factor;
influence on the change in the turnover of the physical volume of turnover (number of goods sold);
the share of the increase in turnover due to changes in prices and the physical volume of turnover.

1. Based on the condition, it is possible to build a multiplicative model for the development of turnover in the reporting year under the influence of the price factor and the factor of the physical volume of turnover: I pq = I р × I q .

2. Using the aggregate form of indices, the resulting model can be transformed as follows:

Σp 1 q 1	=	Σp 1 q 1	×	Σp 0 q 1
Σp 0 q 0	=	Σp 0 q 1	×	Σp 0 q 0

where Σp 1 q 1 is the turnover of the reporting year; Σp 0 q 0 is the turnover of the previous year; Σp 0 q 1 - turnover of the reporting year in the prices of the previous year (turnover in comparable prices).

From here, the scheme for calculating the factors will take the form:

Σp 1 q 1 - Σp 0 q 0 = (Σp 1 q 1 - Σp 1 q 0) + (Σp 1 q 0 - Σp 0 q 0) or ΔΣpq = ΔΣpq p + ΔΣpq q .

where (Σp 1 q 0 - Σp 0 q 0), ΔΣpq p - influence of prices; (Σp 1 q 1 - Σp 1 q 0), ΔΣpq q - quantity effect.

3. Since prices increased by 18% in the reporting year, the price index: I р = 1.18.

4. The turnover in comparable prices will be: Σp 0 q 1 \u003d Σp 1 q 1 / I р \u003d 78300 / 1.18 \u003d 66356 thousand rubles.

5. Calculate the index of the physical volume of the turnover of a trade organization:

I q \u003d Σp 0 q 1 / Σp 0 q 0 \u003d 66 356 / 64 500 \u003d 1.03.

6. The change in the value of the organization's turnover (ΔΣpq) can be calculated by subtracting from the numerator the first fraction included in the model, its denominator:

ΔΣpq \u003d Σp 1 q 1 - Σp 0 q 0 \u003d 78300 - 64500 \u003d 13800 thousand rubles.

This change is obtained as a result of the combined influence of two factors: the factor of prices and the factor of the quantity of goods sold.

7. To reveal the influence of the price factor on the change in the organization's turnover (ΔΣpq p), it follows from the numerator of the second fraction included in the model to subtract its denominator:

ΔΣpq p \u003d Σp 1 q 1 - Σp 0 q 1 \u003d 78300 - 66 356 \u003d +11944 thousand rubles.

Thus, due to the increase in prices by an average of 18%, the trade organization received additional revenue in the amount of 11,944 thousand rubles.

8. To identify the influence of the factor of the physical volume of turnover on the change in the turnover of the organization (ΔΣpq q), it follows from the numerator of the third fraction included in the model, subtract its denominator:

ΔΣpq q \u003d Σp 0 q 1 - Σp 0 q 0 \u003d 66 356 - 64 500 \u003d +1856 thousand rubles.

Thus, due to the increase in the number of goods sold by 3%, the trade organization received additional revenue in the amount of 1856 thousand rubles.

9. Check the correctness of the calculations:

ΔΣpq = ΔΣpq p + ΔΣpq q = 11944 + 1856 = +13800 thousand rubles

10. Calculate the share of the increase in turnover due to the change:

a) prices: D p = ΔΣpq p / ΔΣpq × 100 = +11944 / 13800 × 100 = 85.6%;

b) physical volume of turnover: D q = ΔΣpq q / ΔΣpq × 100 = 1856 / 13800 × 100 = 13.4%.

Consequently, in the reporting year, the increase in the turnover of the trade organization was obtained mainly due to an increase in prices for goods sold.

Elimination is a logical technique in which the influence of one factor is sequentially singled out and the action of all the others is excluded. In other words, to eliminate means to eliminate, exclude the influence of all factors on the value of the effective indicator, in addition, the influence of which is quantified. In this case, it is assumed that all factors change independently of each other, i.e. first, one factor changes, while all others remain unchanged, then the second changes, while the rest remain unchanged, and so on.

The following elimination methods are used: difference method, chain substitution method and integral method.

The method of absolute differences is used only in multiplicative and mixed models. When using it, the absolute difference in the studied factors is preliminarily determined. Then the deviation (difference) for one factor is multiplied by the absolute value of the other factor. In this case, the influence of the extensive factor is first calculated, and then the intensive one.

Any resulting indicator that characterizes the economic activity of an organization can be obtained either by increasing resources (extensively) or by increasing the efficiency of using available resources without additional involvement (intensively). However, as a rule, the result is achieved in both ways at the same time. Therefore, the result obtained can be described by the following model:

where P is the resulting indicator; E - extensive factor; And is an intense factor.

ΔRe \u003d (E 1 - E 0) × I 0 \u003d ΔE × I 0,

where ΔRe is the change in the result due to the influence of the extensive factor; E 0 , E 1 - the values of the extensive factor in the base and reporting periods, respectively; And 0 is the value of the intensive factor in the base period.

In order to calculate the influence of an intensive factor, it is necessary to multiply the change in its value by the value of the extensive factor in the reporting period, but in the reporting period the intensity of the use of available resources will be increased:

ΔRi \u003d (I 1 - And 0) × E 1 \u003d ΔI × E 1,

where ΔРи is the change in the result due to the influence of the intensive factor; And 0 , And 1 - the values of the intensive factor in the base and reporting periods, respectively; E 1 - the value of the extensive factor in the reporting period.

Example 12.2

It is necessary to calculate by the method of absolute differences the influence on the change in the turnover of the retail trade of a trade organization of the factor of change in the trading area and the factor of change in the volume of retail trade turnover per 1 m 2 of the trading area.

For calculations, we use the data in Table. 12.5.

As can be seen from Table. 12.5, in the reporting year, the retail trade turnover increased by 30,335 thousand rubles. This increase is due to the influence of extensive and intensive factors. The extensive factor is the retail space, and the intensive factor is the turnover per 1 m 2 of the retail space. The difference method can be used to calculate the influence of these factors. First you need to write a model for the relationship of the result with the factors. Therefore, we denote the turnover of a trading organization with the letter B (revenue), the extensive factor with the letter S, and the intensive factor with the letter P (sales). At the same time, it must be remembered that the letters for designating the result and factors are selected based on the convenience of the user, no generally accepted designations have been established in this case.

Table 12.5

So, the communication model will look like: B \u003d S × P.

ΔBs \u003d ΔS × P 0 \u003d + 200 × 94.6316 \u003d + 18926 thousand rubles.

2. Factor of change in retail trade turnover per 1 sq. m. of retail space:

ΔВр = ΔР × S 1 = +9.9206 × 1150 = +11409 thousand rubles.

The sum of the influence of factors:

As can be seen from the table and the calculations, in the reporting year, the retail trade turnover of the trade organization increased by 30,335 thousand rubles. This happened primarily due to the increase in retail space. The increase in retail space by 200 m 2 allowed to increase the organization's revenue by 18,926 thousand rubles. It is also positive that in the reporting year the efficiency of the use of retail space increased. The increase in turnover per square meter of retail space allowed to increase the turnover of the trade organization by 11,409 thousand rubles.

At the same time, it should be noted that the turnover of the trade organization developed mainly in an extensive way.

If the extensive and intensive factors are interchanged in the model given in the example, then the calculation results will be different. This means that the order of replacement in the multiplicative model is extremely important for interpreting the results.

Therefore, before proceeding with the calculations, it is necessary:

identify a clear relationship between the studied indicators;
clearly define extensive (quantitative) and intensive (qualitative) indicators;
correctly determine the sequence of substitutions.

Relative difference method is used to measure the influence of factors on the growth of the effective indicator only in multiplicative models.

The calculation of the influence of factors is carried out as follows.

To calculate the influence of the first factor, it is necessary to multiply the base value of the effective indicator by the relative growth of the first factor, expressed as a percentage (growth rate), and divide the result by 100%.

Change in the result due to the extensive factor (ΔRe):

ΔRe = (P 0 × ΔE%) / 100%;

ΔE% \u003d (E 1 - E 0) / E 0 × 100%.

To calculate the influence of an intensive factor, it is necessary to add the change in the effective indicator due to the first factor to the base value of the effective indicator and then multiply the resulting amount by the relative growth of the intensive factor in percent and divide the result by 100%.

Change in the result due to the intensive factor (ΔРi):

ΔRi \u003d (P 0 + ΔRe) × ΔI% / 100%;

ΔI% \u003d (I 1 - And 0) / And 0 × 100%.

Example 12.3

Let's carry out calculations according to the data of the previous example from Table. 12.5.

1. Factor of change in selling area (extensive):

ΔВs = (В 0 × ΔS%) / 100% = 89900 × 21.0526 / 100 = + 18926 thousand rubles.

2. Factor of change in retail trade turnover per 1 m 2 of retail space:

ΔВр = (В 0 + ΔВs) × ΔИ% / 100% = (89900 + 18926) × 10.4834 / 100 = = +11409 thousand rubles.

The sum of the influence of factors:

ΔВ = ΔВs + ΔВр = (+18926) + (+11409) = +30335 thousand rubles.

The method of relative differences can also be used if the number of factors under study is more than two. At the same time, the influence of the third, fourth, etc. factors (if any) is determined similarly to the calculation of the second factor with the addition to the sum of the change in the result due to the influence of the second, third, etc. factors.

This method is very effective in cases where the initial data contain relative changes in factor indicators in percentages or coefficients (indices). It is convenient to use in cases where it is required to calculate the influence a large number factors.

Chain substitution method. The essence of this method of economic analysis lies in the sequential elimination of some factors in order to determine the influence of others, i.e. in the successive replacement of the base value of the factor indicators included in the dependence model (calculation formula) with the actual value (the value of the reporting period) of these indicators. After each replacement, the result of the calculation is compared with the result obtained before replacing this indicator in this formula. The calculated deviations reflect the influence of each factor.

If the indicator is the product of three factors (factors), then the formula for the base indicator will be as follows:

Y 0 \u003d a 0 × b 0 × c 0,

and for the actual indicator:

Y 1 \u003d a 1 × b 1 × c 1.

The change in the performance indicator, on the one hand, can be represented as the difference between its actual and base value, and on the other hand, as the sum of changes in the performance indicator under the influence of individual factors:

Y 1 - Y 0 \u003d ΔY \u003d ΔYa + ΔYb + ΔYc.

To determine the influence of each of the three factors, it is necessary to make the following calculations.

First, the influence of factor a is calculated. To do this, in the basic model, we replace the basic value of this factor with its actual value:

Y 2 \u003d a 1 × b 0 × c 0;
Y 0 \u003d a 0 × b 0 × c 0.

These calculation formulas differ only in the value of the factor a, the value of the other factors does not change. Therefore, if we subtract the base indicator (Y 2) from the obtained conditional indicator (Y 2), then the result obtained will show the influence of the first factor on the change in the resulting indicator:

Y 2 - Y 0 \u003d ΔYa.

Then sequentially, i.e. from right to left, in the formula Y 2 we will replace the basic value of the next factor (factor "b") with its actual value and get the following conditional indicator Y 3 . It differs from Y 2 only by the value of the factor "b":

Y 3 \u003d a 1 × b 1 × c 0;
Y 2 \u003d a 1 × b 0 × c 0.

Y 3 - Y 2 \u003d ΔYb.

In the following formula, we replace the basic value of the factor c with the actual one and obtain the formula Y 1 , which differs from Y 3 only by the value of the factor c:

Y 1 \u003d a 1 × b 1 × c 1;
Y 2 \u003d a 1 × b 0 × c 0.

Y 1 - Y 3 \u003d ΔYc.

factor of change in trading area;
factor of change in the number of working days;
factor of change in the volume of the average daily turnover of retail trade per 1m 2 of retail space.

For calculations, we use the data in Table. 12.6.

Table 12.6

First, you need to write a model of the relationship between performance and factor indicators. It will look like this:

B = S × D × R.

Therefore, the retail trade turnover calculation model looks like:

in the base year: B 0 \u003d S 0 × D 0 × R 0;
in the reporting year: B 1 \u003d S 1 × D 1 × R 1.

From the models obtained, it can be seen that the development of retail trade turnover in the reporting year was influenced by three factors.

We calculate the influence of each factor separately. To calculate and quantify the influence of factors, we use the chain substitution method.

1. The basic value of the retail trade turnover of the organization under study can be calculated using the formula B 0 \u003d S 0 × D 0 × P 0. As can be seen from Table. 12.6, its value was 89900 thousand rubles.

2. Then, in this formula, we replace S 0 with S 1 and get the value of the retail trade turnover, provided that the area is the reporting year, and the number of working days and the average daily retail trade turnover per 1 m 2 of retail space - the base:

B 2 \u003d S 1 × D 0 × R 0 \u003d 1150 × 310 × 0.3053 \u003d 108826 thousand rubles.

Hence, the influence of the selling area factor will be:

ΔВs \u003d B 2 - B 0 \u003d S 1 × D 0 × R 0 - S 0 × D 0 × R 0 \u003d (S 1 - S 0) × D 0 × R 0 \u003d 108826 - 89900 \u003d +18926 thousand rubles.

Thus, we can conclude that the retail space factor had a positive impact on the change in the turnover of the trade organization, since by increasing the area by 200 m 2 it created the prerequisites for increasing turnover by 18926 thousand rubles.

In formula B 2, we replace D 0 with D 1 and get the conditional value of retail trade turnover based on the fact that the area and number of working days will be the same as in the reporting year, and the average daily retail trade turnover per 1 m 2 of retail space will be as follows same as in the base:

B 3 \u003d S 1 × D 1 × R 0 \u003d 1150 × 305 × 0.3053 \u003d 107071 thousand rubles.

Hence, the influence of the factor of the number of working days will be:

ΔV D \u003d B 3 - B 2 \u003d S 1 × D 1 × R 0 - S 1 × D 0 × R 0 \u003d S 1 × (D 1 - D 0) × R 0 \u003d 107071 - 108826 \u003d -1755 thousand rubles .

As can be seen from the calculation, the reduction in the number of working days in the reporting period, compared with the base period, by 5 days created the prerequisites for a decrease in the turnover of the trade organization by 1,755 thousand rubles.

4. Then, in the formula B 3, we replace P 0 with P 1 and get the actual retail turnover in the reporting year: B 1 \u003d S 1 × D 1 × R 1.

Data on the value of this turnover can be taken from Table. 12.6. The actual turnover of the trade organization in the reporting year amounted to 120,235 thousand rubles.

Hence, the influence of the factor of the average daily turnover of retail trade per 1 m 2 of retail space will be:

ΔВp \u003d B 1 - B 3 \u003d S 1 × D 1 × R 1 - S 1 × D 1 × R 0 \u003d S 1 × D 1 × (P 1 - P 0) \u003d 120235 - 107071 \u003d +13164 thousand rubles.

Thus, from Table. 12.6 it can be seen that in the reporting year, the efficiency of the use of retail space has increased. If in the base year the average daily turnover received by a trade organization from each square meter trading area, amounted to 0.3053 gys. rubles, then in the reporting year - 0.3428 thousand rubles. Increase in turnover from one square meter of retail space by an average of 0.0375 thousand rubles per day.

5. Cumulative influence of factors:

ΔВ = ΔВs + ΔВд + ΔВр = (+18926) + (-1755) + (+13164) = +30335 thousand rubles, which corresponds to the data in Table. 12.6.

It should be noted that this method of analysis is used only when the relationship between the studied phenomena is represented as a direct or inversely proportional relationship. In these cases, the analyzed aggregate indicator as a function of several variables should be displayed as a product or quotient of dividing some indicators by others.

The advantages of this method are the versatility of application, ease of calculation.

The disadvantage of chain substitution is that, depending on the chosen order of factor replacement, the results of the factor expansion have different values. This is due to the fact that as a result of applying this method, a certain indecomposable residue is formed, which is added to the magnitude of the influence of the last factor or distributed among the influence of all qualitative factors. In practice, the accuracy of the assessment of factors is neglected, highlighting the relative importance of the influence of a particular factor. However, there are rules governing the sequence of substitution:

if there are quantitative and qualitative indicators in the factor model, the influence of quantitative factors is considered first of all;
if the model is represented by several quantitative and qualitative indicators, the substitution sequence is determined by logical analysis.

For example, the annual volume of production (B) on the equipment of the i-th group can be considered as the product of the number of pieces of equipment (Ki) and the annual productivity of a piece of equipment (GPi), t.s. be described by the following model:

B \u003d Ki × GPi,

where Ki is an extensive (quantitative) factor; GPi is an intensive (qualitative) factor.

In turn, the annual productivity of a piece of equipment depends on the number of working days (D) and the daily productivity of a piece of equipment DPi, where the first factor will also be extensive, and the second - intensive. From here, the original model will take the form:

B \u003d Ki × D × DPi.

Daily productivity can also be considered as the product of an extensive factor - the shift coefficient (Kcm), and an intensive factor of shift productivity SPi. Therefore, the annual production volume can be described by the model:

B \u003d Ki × D × Kcm × SPi

balance method economic analysis is used in the study of the influence of factors on a certain performance indicator, provided that all of them are interconnected in the balance formula. The method consists in comparing, commensurate two sets of indicators tending to a certain balance. It allows you to identify as a result a new analytical (balancing) indicator. Balance linking of various indicators is needed to study certain aspects of the economic activity of organizations. With the help of this technique, the ratio of the availability and receipt of commodity funds with their use is analyzed, etc.

For example, the balance of goods has the formula

Zn + P \u003d R + B + Zk,

where Зн and Зк - stocks of goods at the beginning and end of the study period; P - receipt of goods; B - other disposal of goods (natural loss, damage, return of goods to suppliers, etc.); P - the volume of sales of goods (revenue).

Based on the commodity balance model, it is possible to identify the influence of factors on the volume of sales of goods in physical or value terms. To do this, based on the commodity balance model, first, the sale of goods in the reporting period is calculated, then in the base period, and then the difference is calculated for each element of the commodity balance:

R 1 × (Zn 1 + P 1 - V 1 - Zk 1) - R 0 × (3n 0 + P 0 - V 0 - Zk 0) \u003d ΔR \u003d ΔZn + ΔP - ΔV - ΔZk.

Thus, from the model characterizing the change in the resulting and factor indicators, one can immediately see not only the change in the result of the organization's economic activity, but also the influence of each of the studied factors on it.

Example 12.5

Table data. 12.7 characterize the elements of the commodity balance of a trading organization in the past and reporting periods.

Table 12.7

Necessary:

using the balance linking method, calculate the influence of factors on the change in the volume of sales of goods in the reporting period compared to the previous year;
analyze the results.

As can be seen from Table. 12.7, the influence of factors on the change in the retail trade turnover of a trading organization is calculated by the comparison method, which leads to an incorrect assessment of the influence of a number of factors (other disposal, stocks of goods at the end of the year). Therefore, it is better to use the balance method (amounts in thousand rubles):

73864 (5149 + 74578 - 520 - 5343) - 71401 (5344 + 71842 - 630 -5149) = +2457 = (-195) + (+2736) - (-100) - (+194)
or
+2457 = -195 + 2736 + 100 - 194.

From the calculations performed, the true influence of the factors can be seen. Retail trade turnover increased under the influence of an increase in the receipt of goods and a decrease in other disposal of goods, a negative impact on the dynamics of turnover had a decrease in stocks of goods at the beginning of the period and their increase at the end of the period.

When using the balance method in the process of economic analysis of the provision of the organization with raw materials, the need for raw materials, the sources of covering the need are compared and a balancing indicator is determined - a shortage or excess of raw materials. This method analyzes the use of working time (balance of working time), the use production capacity(balance of production capacity), balance of labor resources, etc.

As an auxiliary, the balance method is used to verify the results of calculations of the influence of factors on the effective aggregate indicator. If the sum of the influence of factors on the effective indicator is equal to its deviation from the base value, then, therefore, the calculations were carried out correctly. The lack of equality indicates an incomplete consideration of factors or mistakes made:

∆Y =	n	ΔY(x i)
	Σ
	i=1

where ΔY is the change in the effective indicator; xi are factors; ΔY(x i) is the change in the effective indicator due to the factor x i .

The balance method is also used to determine the size of the influence of individual factors on the change in the effective indicator, if the influence of other factors is known.

The balance method of analysis can be used when studying the financial position of an organization. With it, based on balance sheet compare liability data (sources of funds) with asset data (composition and placement of funds), establish the correct use of funds, bank loans, etc.

Integral method. The disadvantage of the method of differences and the method of chain substitution, as already mentioned, is that the results of the calculations depend on the sequence of replacement of factors and the indecomposable remainder is often unreasonably attributed to the influence of a change in the qualitative factor. This shortcoming is eliminated by using the integral method. It does not require the use of methods for the distribution of the indecomposable remainder among the factors, since the logarithmic law of the redistribution of factor loads operates in it. The integral method allows you to achieve a complete decomposition of the effective indicator by factors and is universal in nature, i.e. applicable to multiplicative, multiple, and mixed models. The operation of calculating a definite integral is reduced to constructing integrands that depend on the type of function or model of the factorial system.

This method is objective, since it excludes any assumptions about the role of factors before the analysis, the provision on the independence of factors is observed.

Using this method allows you to get more accurate calculation results that do not depend on the location of the factors: the change in the resulting factor is proportionally decomposed between the factors.

If the influence of two factors on the performance indicator is studied, then the formula can be used for calculation:

The calculation of the influence of factors is carried out according to the formulas:

ΔYa = b 0 × Δа + (Δа × Δb)/2 ;
ΔYb = a 0 × Δb + (Δa × Δb)/2 .

Non-formalized methods of economic analysis

Expert diagnostics is understood as means of analysis based on the generalization of assessments and information given by experts. This method is used when it is necessary to choose a solution that cannot be determined on the basis of exact calculations. Such situations often arise in the development contemporary problems production management and, most importantly, in forecasting and long-term planning. The essence of the method of expert assessments is that experts conduct an intuitive-logical analysis of the problem with a quantitative assessment of judgments and formal processing of the results. The generalized opinion of experts received as a result of processing is accepted as one of the options for solving the tasks facing the organization. The complex use of intuition (unconscious thinking), logical thinking and quantitative assessments with their formal processing makes it possible to obtain an effective solution to the problem.

Thus, this method of analysis is based on information often obtained by contact methods through special expert surveys and expert assessments obtained on their basis.

Expert assessments are quantitative or ordinal assessments of processes or phenomena that cannot be directly measured. They are based on expert opinion. In principle, therefore, they cannot be considered completely objective, since various side factors can affect a specialist expert. At the same time, the active and purposeful participation of specialists in every stage of managerial decision-making makes it possible to improve their quality and efficiency.

In the process of conducting the analysis, experts use questionnaire methods and methods of group examination.

The advantages of these methods are the simplicity of organization, the possibility of using statistical data processing, the possibility of covering large groups of information.

Among the shortcomings, one can single out the incompleteness of the answers, the subjective factor of the respondents, the possibility of misunderstanding of the questions by the experts.

To process the subjective opinions of experts, various methods are used, the main of which is ranking.

Ranking involves ordering the evaluated objects in ascending or descending order of their qualities. Ranking can be carried out by several methods, but each of them is based on expert opinions - the judgments of specialists about the object being evaluated.

The most common ranking method is soft rating. According to this method, the experts leave in the list, without indicating the priority, the best, from their point of view, evaluated objects. The object with the highest number of expert votes gets the highest rank.

Another way to conduct a rating assessment is direct ranking. The essence of this method lies in the fact that the experts arrange the assessed objects in a certain order (as a rule, ascending or descending qualities), then the arithmetic mean place of each object is calculated and, in accordance with this value, a finally ordered list is compiled. The reliability of the results of the examination is checked according to the value of the coefficient of concordance - the consistency of the methods of experts.

A more complex ranking method is a pairwise comparison, according to which experts, comparing each two assessed objects in turn, determine which of them is better, then these opinions are averaged and the final rating is compiled according to the rule: “If A is better than B, B is better than C, then And C is better. The problem of applying this method is related to the fact that experts have to analyze a large number of pairs, while averaging can lead to a logical dead end: "A is better than B, B is better than C, C is better than A". In addition, direct ranking cannot be applied if the list of ranked objects is left open.

When using the ranking method based on a score, the list of evaluated objects can be unlimited. Experts themselves name the number of objects and evaluate them in points or arrange them in a certain order, while the corresponding number of points is assigned to the ordinal number. To obtain a finally ordered list of ranked objects, the scores are added up, and the objects are arranged in ascending or descending order of scores.

The main problem of ranking as one of the evaluation methods is related to the fact that comparisons of objects are carried out according to several indicators and the results can be ambiguous: the leader in one indicator can become an outsider in another (a classic example: high profitability of corporate securities with a high degree of investment risk).

Therefore, there is a rating in which objects are ranked separately for each indicator. The right to determine which of the ranked qualities is the most important is given to the one who uses the ranking results. Attempts are also being made to harmonize ranked lists based on elementary methods for calculating weighted averages, taking into account the weighting coefficients (importance for analysis) of indicators or a special mathematical and logical apparatus.

Varieties of the method of expert assessments are:

the method of "brainstorming" (the emergence of ideas occurs in a creative dispute and personal contact of specialists);
the method of "brainstorming" (when one group of experts puts forward an idea, and another analyzes it);
method "delphi" (provides an anonymous survey of a specialist on pre-prepared questions with subsequent processing of answers).

The process of developing managerial decisions depends on the level information support, the ability to analyze the received data and synthesize possible solutions based on them. The situational approach allows effective management of a specific situation of making a managerial decision.

Situational analysis is a complex process that allows you to justify the adoption of a managerial decision, which is based on the analysis of a single managerial situation. In the process of situational analysis, the method of induction is used, the analysis begins with the study of specific situations, problems that arise in the activities of the organization, on which a managerial decision must be made.

Situational analysis allows, based on a deeper study of situations, the establishment of trends, patterns and factors that determine their development, to justify strategic management decisions up to the adjustment of the strategic goals of the organization.

One of the main problems solved by situational analysis is the establishment of factors that determine the development of the situation. At the same time, it is important to establish not all, but namely the main factors that have a significant impact on the development of the situation, and discard those factors that cannot have a significant impact.

To identify the main factors in the process of analyzing a particular situation, various techniques are used, among which are:

method of "brainstorming";
two-round survey method.

Brainstorming in situational analysis is usually carried out in two stages: the first stage is the generation of ideas, and the second stage is the discussion of the identified ideas, their evaluation and the development of a collective point of view. At the second stage, the so-called court method can be used: the experts involved in the analysis are divided into supporters and opponents of the opinion expressed.

A two-round survey involves the individual work of specialists to identify the most important, basic factors that determine the development of the situation. In the first round, each of the specialists fills out a specially designed questionnaire, in which they indicate the main factors and justify the reasons for classifying these factors as the main ones. The factors included in the questionnaire are ranked by the specialist according to the degree of their influence on the development of the situation. In the second round, a cross-review of the questionnaires completed in the first round is carried out. This means that questionnaires filled out by one specialist are evaluated by others and agree or disagree with the assessments made by him. The results of the second round are processed by the analytical group, which, on the basis of the data presented in the questionnaires, forms a list of factors that, according to experts, determine the development of the situation.

In a situational analysis, various modeling methods can be used:

analogue models, which model, for example, the organizational structure and the flow of commands;
mathematical models that allow you to track the development of the situation by establishing accurate dependencies, for example, the relationship between production volumes and costs.

With their help, the problems of resource allocation in strategic management and many other tasks can be solved; game theory models, etc.

Conducting a situational analysis and making managerial decisions on its basis, it is impossible to unambiguously determine the direction in which the situation will develop. However, it makes it possible to foresee the most probable scenarios for the development of the situation, to prepare the most preferable alternative solutions in each of the possible directions of the development of the situation. A scenario is a predominantly qualitative description of possible options for the development of an object under study under various combinations of certain predetermined conditions. The scenario method is not intended for forecasting, it only has to show in a detailed form the possible scenarios for the development of events for their further analysis and selection of the most realistic one.

Methods of situational and scenario analysis are closely related to the method of SWOT-analysis.

SWOT is an acronym for Strengts (strengths), Weaknesses (weaknesses), Opportunities (opportunities), and Threats (threats). The internal environment of the company is reflected mainly in S and W, and the external environment - in O and T. The method of SH-analysis allows, on the one hand, to identify the internal strengths and weaknesses of the organization's activities, and on the other hand, external opportunities and threats, and establish links between them.

The classic presentation of information from such an analysis is the compilation of a table of strengths in the organization's activities, its weaknesses, potential favorable opportunities and external threats (Table 12.8).

Table 12.8

At the intersection of SW with OT, an expert assessment of their mutual influence in points is put down. The total score for rows and columns shows the priority of taking into account one or another factor in the formation of a strategy.

Based on the results of the SWOT analysis, a matrix of strategic measures is compiled:

steps to take in order to use strengths to increase the capacity of the organization;
activities that need to be carried out, overcoming weaknesses and using the opportunities presented;
activities that will use the strengths of the organization to eliminate threats;
activities that minimize the weaknesses of the organization to avoid threats.

When using the SWOT analysis method, several rules must be observed:

specify the scope of the SWOT analysis as much as possible. When conducting a business-wide analysis, the results are likely to be too general and useless for practical application;
correctness in attributing one or another factor to strengths/weaknesses or opportunities/threats;
use of versatile objective information.

SWOT-analysis is only a tool for structuring the available information, it will not give clear and well-formulated recommendations, specific answers. It only helps to visualize the main factors, as well as to evaluate, as a first approximation, the mathematical expectation of certain events.

The simplicity of the SWOT analysis is deceptive; its results depend on the completeness and quality of the initial information. Mistakes made during the formation of the table (inclusion of unnecessary factors or loss of important ones, incorrect assessment of weight coefficients and mutual influence) are difficult to detect in the process of further analysis and lead to incorrect conclusions, and hence erroneous strategic decisions.

SWOT analysis can be deepened using the PEST analysis method.

PEST analysis is an analysis method that allows you to identify political (Policy), economic (Economy), social (Society) and technological (Technology) environmental factors that may affect the organization's strategy. Politics is studied because it regulates power, which in turn determines the organization's environment and the receipt of key resources for its activities. The main reason for studying economics is to create a picture of the distribution of resources at the state level, which is the most important condition for the operation of an organization. Equally important consumer preferences are determined using the social component of PEST analysis. The purpose of the study of the technological component is to identify and study trends in technologies that change in the process of scientific and technological progress and are often the causes of changes and market losses, as well as the emergence of new products.

Functional cost analysis (FCA) is a method of feasibility study of systems aimed at optimizing the relationship between their consumer properties (the ability to meet certain user needs) and the costs of creating these properties. In other words, functional cost analysis is a method of systematic research of the functions of an individual product or a certain production and economic process, or a management structure, aimed at minimizing costs at the stages of design, development of production, marketing, industrial and domestic consumption at a certain quality, marginal utility and durability.

Functional cost analysis is an effective way to identify reserves to reduce costs, which is based on the search for cheaper ways to perform the main functions (through organizational, technical, technological and other changes in production) while eliminating unnecessary functions.

The ultimate goal of functional cost analysis is to find the most economical options for a particular practical solution from the point of view of the consumer and the manufacturer.

The FSA method allows you to reorganize activities in such a way that a sustainable reduction in cost, labor intensity and time is achieved. To do this, do the following:

form a ranked list of functions by cost, labor intensity or time;
select functions with high cost, labor intensity and time consumption;
eliminate unnecessary features;
reduce the time required to perform functions;
organize the sharing of all possible functions;
reallocate resources freed up as a result of improvements.

These actions improve the quality of business processes. In addition, improving the quality of business processes is carried out by conducting a comparative assessment and choosing rational (according to cost or time criteria) technologies for performing operations or procedures that are elements of business processes.

Functional cost analysis is based on the following statement: each product, object, etc. produced, exists in order to satisfy certain needs (perform its functions). A more detailed examination of any object, you can see that it performs not one, but always many functions. In the process of analysis, they can be divided into basic, auxiliary and superfluous (unnecessary or generally harmful). However, in any case, the creation of these functions in the subject is associated with certain costs. From this, it becomes obvious that if the functions are not needed, then the costs of their creation are also unnecessary. Therefore, the functional cost analysis divides all costs into functionally necessary for the object to fulfill its functional purpose and into unnecessary ones, generated by the wrong choice or imperfection of design solutions.

Moreover, each function performed by the object of study can be implemented in different ways. different ways the implementation of the function depends on the applied technological and technical solutions and, accordingly, are associated with different amounts of costs. This allows you to choose a way to implement a certain function, which will also minimize the cost of its creation. Thus, the replacement existing method performance of the function cheaper, a reduction in the cost of the product is achieved.

In order to ensure the greatest return on the use of the FSA method, it is necessary to observe a number of principles for conducting an analytical study:

the principle of early diagnostics, the essence of which is that the value of the identified reserves depends on at what stage of the life cycle of the product the analysis is carried out: pre-production, production, operation, disposal. As a rule, excessive costs are mainly laid down at the design stage;
the principle of optimal detail. The main meaning of the FSA is the allocation of consumer functions of the object of study (product, process). However, if the object under study is sufficiently complex, then as a result of its division into separate functions, too many of them may be formed. Such narrow detail complicates the analysis and reduces its effectiveness. Therefore, it is advisable to first divide the object of study into large parts (individual product units, separate groups of technological operations, and then, for a deeper study, single out smaller objects in them);
the principle of sequence provides for the use of a certain logical scheme of detail - from the general to the particular (object - node - function). At the same time, the results of the analysis at each stage depend on the completeness and quality of the study at the previous stages;
the principle of highlighting the leading link assumes that in any object of study (product, process) there is some part that requires a lot of money to ensure the viability of this object or hinders the receipt of the effect from its functioning (use). Therefore, in the process of research, it is advisable to focus on this particular part of the object of analysis.

Thus, functional cost analysis is an important tool improving the efficiency of economic activity, strengthening the competitiveness of products, resource saving.

Economic and mathematical methods of analysis

The use of economic and mathematical methods expands the possibilities of economic analysis by reducing the time of analysis, assessing the impact of more factors on the results of the economic and financial activities of the organization, increasing the accuracy of assessing their impact, setting and solving multidimensional analysis problems, which is especially important when conducting prospective and strategic analysis, whose role is currently growing.

In economic analysis, mathematical models are used that describe the phenomena and processes under study using equations, inequalities, functions, and other mathematical tools. The economic-mathematical model, adequate to reality, makes it possible to identify the essential aspects and relationships of the object under study.

Economic and mathematical methods widely used in economic analysis include the method of correlation and regression analysis; econometric methods, game theory, queuing theory, mathematical programming methods, inventory optimization method (Wilson model), etc.

Correlation analysis is based on the use of probabilistic models that describe the behavior of the studied features in a certain general population, from which the experimental values are obtained. Correlation is a statistical relationship between two or more random variables. In this case, a change in the values of one or more of these quantities is accompanied by a systematic change in the values of another or other quantities. A mathematical measure of the correlation of two random variables is the linear correlation coefficient (Pearson's correlation coefficient).

This method of analysis allows, based on the use of a sufficiently large array of economic information, to identify and quantify the links between economic phenomena, to assess the closeness of these links and, on this basis, to identify the main and secondary factors that caused this or that economic phenomenon, process.

In the process of correlation analysis, the following tasks are solved:

establishing the form and direction (positive or negative) of the relationship between varying features (linear, non-linear);
measuring the closeness of the connection and checking the degree of significance of the obtained correlation coefficients.

Correlation analysis is most often used to establish relationships between economic indicators that are not in functional, but in stochastic dependence, i.e. when a change in one economic indicator does not cause a certain and inevitable change in another.

Correlation analysis allows you to identify trends in economic phenomena, build a mathematical model of the patterns of change in the main indicator (function) due to changes in factors (arguments). This pattern is called regression, and the analysis of its properties (search for functional dependencies y(x), whose graphs are the central lines of the data correlation field) is called regression analysis of the correlation.

Regression analysis is a statistical method for studying the influence of one or more independent variables on a dependent variable. Independent variables are otherwise called regressors or predictors, and dependent variables are called criteria.

Goals of regression analysis:

determination of the degree of determination of the variation of the criterion (dependent) variable by predictors (independent variables);
predicting the value of the dependent variable using the independent variable(s);
determination of the contribution of individual independent variables to the variation of the dependent variable.

The correlation analysis scheme includes several stages:

collection of information, its arrangement in a certain sequence (in ascending, descending and other signs), grouping. Qualitative analysis of indicators, the nature of the relationship between which is being studied;
logical analysis of empirical data on the change in the effective indicator and the values of the factor influencing it, which allows us to make assumptions about the presence and direction of the relationship between the sign and the factor;
graphical analysis: data are placed as points on a coordinate plane. The coordinates of the points are determined by the corresponding values of the pairs of variables (x, y). The set of obtained points is called the correlation field. By connecting the points in series on the graph, a broken line is built, which is an empirical regression line. By its appearance, one can judge the form of the relationship between economic phenomena and suggest the type of theoretical regression line;
choice of the constraint equation;
verification of the compliance of the expected function with the actual data by calculating the correlation coefficient, residual variance, constructing a confidence interval, etc.

In the event that the regression model is stable over time, it can be used to conduct a prospective analysis and solve problems of predicting changes in the effective indicator.

Cluster analysis is used in the study of multidimensional statistical populations. Its essence lies in the division of the set of studied objects and features into homogeneous groups or clusters. Cluster analysis allows you to group research objects not by one parameter, but by several criteria. It allows you to consider a sufficiently large amount of information, compress arrays of socio-economic information, make them compact and visual. An important issue when using this method is the choice of criteria for the formation of groups of objects, since in this case the individual features of individual objects may be lost due to their replacement by the characteristics of the generalized values of the cluster parameter.

In the process of cluster analysis, it is necessary, on the basis of the data contained in the set X, to divide into a set of objects G into m clusters (subsets) Qm so that each object G belongs to only one partition subset and that the objects belonging to the same cluster are similar, while objects belonging to different clusters were heterogeneous.

Game theory is a theory of mathematical models for making optimal decisions under conditions of uncertainty or conflict of several parties with different interests. Game theory allows you to explore conflict situations and, on the basis of this, develop recommendations for the most rational course of action for each of the participants in the course of a conflict situation. Formalizing conflict situations mathematically, they can be represented as a game of two, three or more players, each of which pursues the goal of maximizing its own benefit, its gain at the expense of the other. The solutions obtained with the help of game theory are useful in the prospective analysis of possible actions in the face of possible opposition from competitors or uncertainty in the external environment.

A game scheme can be given to many situations in the economy. Here the payoff can be the efficient use of scarce resources, production assets, profit margin , cost price, etc. Game theory can also be used to select the optimal solution, for example, when creating stocks of raw materials, semi-finished products. In this case, two tendencies oppose: an increase in stocks, including insurance ones, guaranteeing the uninterrupted operation of production, and a reduction in stocks, minimizing the cost of their storage.

Methods and recommendations of game theory are developed in relation to such specific conflict situations that have the property of repeated repetition. If the conflict situation is realized once or a limited number of times, then the recommendations of game theory lose their meaning.

To solve problems, algebraic methods based on a system of linear equations of inequalities, iterative methods, as well as reducing the problem to a system of differential equations are used.

In order to analyze a conflict situation according to its mathematical model, the situation must be simplified, taking into account only the most important factors that significantly affect the course of the conflict.

The theory of queuing studies systems designed to service a mass flow of requirements of a random nature (both the moments of the appearance of requirements and the time spent on their service can be random). She explores, on the basis of probability theory, mathematical methods for quantifying queuing processes. The purpose of the research is to rationally choose the structure of the service system and the service process based on the study of the flow of service requirements entering and exiting the system, the waiting time and the length of the queues. Queuing theory uses methods from probability theory and mathematical statistics. In this case, chronometric observations are often required for customer service. The purpose of the analysis may be to determine the probability of refusal to provide certain services or requests.

A typical example of objects of the queuing theory can be automatic telephone exchanges, which randomly receive “requests” calls from subscribers, and “service” consists in connecting subscribers to other subscribers, maintaining communication during a conversation, etc.

Using the methods of queuing theory allows you to organize a service that provides a given quality.

In queuing systems (QS) the serviced object is called a requirement. In the general case, a requirement is usually understood as a request to satisfy some need, for example, a conversation with a subscriber, landing an airplane, buying a ticket, buying goods in a store, etc.

The means that serve the requirements are called service devices or service channels. For example, these include telephone communication channels, cash registers in store settlement centers, landing strips, ticket clerks, etc.

In the theory of queuing, such cases are considered when the receipt of requirements occurs at random intervals, and the duration of the service of requirements is not constant, i.e. is random. For these reasons, one of the main methods of mathematical description of QS is the apparatus of the theory of random processes.

The main task of the theory of queuing is to study the mode of operation of the serving system and the study of phenomena that occur in the process of servicing.

So, one of the characteristics of the serving system is the time spent by the requirement in the queue. Obviously, this time can be reduced by increasing the number of service devices. However, each additional device requires certain material costs, while the idle time of the service device increases due to the lack of maintenance requirements, which is also a negative phenomenon. Therefore, in the theory of queuing, optimization problems arise: how to achieve a certain level of service (maximum reduction in the queue or loss of customers) at the minimum cost associated with the downtime of service devices.

Econometric methods are based on the synthesis of three areas of knowledge: economics, mathematics and statistics. The basis of econometrics is an economic model, which is understood as a schematic representation of an economic phenomenon or process using scientific abstraction, reflecting them characteristic features. With the help of econometric methods, it is necessary to evaluate various quantities and dependencies used in the construction of simulation models of various processes, for example, when analyzing payment flows, it is advisable to use econometric models of inflationary processes in order to establish the real ratio of advance and final payments.

Econometric models can be used for perspective and strategic analysis of macroeconomic indicators. These are multivariate time series forecasting models that evaluate both the structure of the model, i.e. the form of the relationship between the values of the known coordinates of the vector at the previous moments of time and their values at the predicted moment, as well as the coefficients included in this relationship.

Econometric methods are an effective tool in the work of a manager dealing with specific problems, designed to analyze statistical data and build econometric models of specific economic and technical and economic phenomena and processes. Most common in modern economy received the method of analysis of the economy "cost - output". These are matrix (balance) models built according to a chess scheme and allowing in the most compact form to present the relationship between costs and production results.

Mathematical programming methods are the main means of solving problems of optimizing production and economic activities. In essence, these methods are means of planned calculations. Their value for economic analysis lies in the fact that they make it possible to assess the intensity of planned targets, to determine the limiting groups of equipment, types of raw materials and materials, to obtain estimates of the scarcity of production resources, etc.

There are the following branches of mathematical programming: linear, parametric, non-linear and dynamic programming. The most developed and widely used section of mathematical programming is linear programming, the purpose of which is to find the optimum (max, min) of a given linear function in the presence of constraints in the form of linear equations or inequalities. Linear programming is a mathematical technique used to determine the best combination of resources and actions required to achieve an optimal result.

Linear programming is the most commonly used optimization technique. Linear programming problems include:

rational use of raw materials and materials; optimization of the production program of enterprises;
optimal location of production;
drawing up an optimal plan for transportation, transport operation;
many others that lie in the field of optimal planning.

For a large number of practically interesting problems, the objective function is expressed linearly - through the characteristics of the plan, and the admissible values of the parameters are subject to linear equalities or inequalities. Finding the absolute extremum of the objective function under given conditions is called linear programming.

The direct problem of linear programming is a mathematical formulation of the problem of drawing up such a plan for the use of various methods and factors of production, which allows you to get the maximum amount of a homogeneous product with the available resources.

Dynamic programming is a computational method for solving control problems of a certain structure, when a problem with n variables is presented as a multi-step decision-making process. At each step, the extremum of the function of only one variable is determined. In this case, the study goes through three stages:

building a mathematical model;
solution of a managerial problem;
analysis and generalization of the obtained results.

Mathematical models of inventory management allow you to find the optimal level of inventory of a certain product, minimizing the total cost of purchasing, placing and delivering an order, storage. The Wilson model is the simplest inventory management model and describes the situation of purchasing products from a supplier, which is characterized by the following assumptions:

consumption intensity is a known and constant value;
the order is delivered from a warehouse where a sufficient stock of goods is stored;
the delivery time of the order is a known and constant value;
each order is shipped as one batch;
the cost of the order does not depend on the size of the order;
the cost of holding the stock is proportional to its size;
lack of stock (shortage) is unacceptable.

The main task of the formation of commodity stocks in trade is to ensure an uninterrupted process of selling goods, or an adequate supply of raw materials and materials ensures the continuity of the production process.

In general, inventory management includes their analysis, planning and operational movement. These tasks can be solved using methods and models of the inventory management theory. The purpose of this theory is to develop methods and models for choosing such control parameters under which the optimum of some criterion is achieved (maximum profits, min costs, etc.).

The formation of commodity stocks is associated with the expenditure of funds. Their value depends primarily on two factors: the frequency of importation of goods and the size of the stock held by the organization. Thus, the total costs of inventory management are the sum of the costs of importing goods and the costs of storing goods in the enterprise. Based on this, the main task of normalizing inventory is to determine such a planned volume of stock of goods at which these total costs would be minimal, i.e. min distribution costs can be taken as an optimality criterion.

The economic and mathematical model of the problem (Wilson's deterministic one-item model) has the following form:

where F(S) - total costs for the supply and storage of goods; Q - the planned volume of turnover for the sale of goods; c - the cost of storing a unit of goods during the entire planning period; k - the cost of importation (purchase and delivery) of one consignment of goods; S is the size of the delivery.

If you use other letter designations, then:

where L is the total cost of supply and storage of goods; V - the planned volume of turnover for the sale of goods; k - the cost of storing a unit of goods during the entire planning period; s is the cost of importation (purchase and delivery) of one consignment of goods; Q is the size of the delivery.

The stock level cycles in the Wilson model are graphically presented in fig. 12.1.

The maximum number of products that are in stock is the same as the order quantity Q.

The cost schedule for inventory management in the Wilson model is shown in Fig. 12.2.

In practice, deviations of the actual values of inventory management parameters from the calculated ones are possible. In this case, it is necessary to evaluate the impact of errors in determining the parameters on the costs of inventory management, i.e. determine such limits of parameter deviations that would not lead to a significant increase in inventory management costs. Therefore, it is required to determine the relative increase in inventory management costs (b) when:

deviation of the actual size of the supply from the optimal (a);
the deviation of the calculated costs for the delivery of one consignment of goods (either the cost of storing a unit of goods, or demand) from the actual ones (g).

In economic analysis, the Wilson model is used to study the deviations of the actual distribution costs from those planned according to the plan, for a prospective analysis of the costs of production and circulation of products.

Graphical method of economic analysis

For a visual representation of economic and mathematical models, graphs are used. Graphs make it easier to understand economic and mathematical models and the economic (economic) phenomena and processes reflected with their help.

A graph is a visual representation of analytical indicators using geometric lines and figures (diagrams). Graphs are usually built on the basis of data from statistical tables. Statistical tables are highly informative and, to a certain extent, visual. However, understanding their digital content takes time, thoughtful work with numbers, and serious comparative analysis. The graphic representation of even the most complex statistical indicators makes them not only visual, but also intelligible and backward at first sight. The graph allows you to quickly catch the most important trends and patterns of the phenomenon under study. Unlike the table underlying it, it gives a substantive generalizing picture of the state of the phenomenon under study, allows you to practically immediately notice its features contained in numerous quantitative indicators, see the trends in its change, identify relationships with other phenomena and processes, and even suggest its possible development in the future.

Graphical models not only make it possible to describe the connection between phenomena, but also to give a quantitative and qualitative characteristic of this connection. At the same time, the possibility of using graphs is limited by the number of spatial dimensions known to mankind.

An important and rather complicated issue of plotting is the division of the entire set of variables into dependent and independent ones.

An independent variable (cause) is a variable that causes a change in another - dependent - variable. In turn, a dependent variable is a variable (result) that changes under the influence of a change in some other, independent variable.

The independent variables are usually shown on the x-axis (horizontal) on the graphs, while the dependent variables are shown on the y-axis (vertical). In some cases, for the convenience of reading the graph, independent variables can be shown on the Y axis, and dependent variables on the X axis (for example, when studying supply and demand curves).

Graphs depicting the relationship of two variables ignore the influence of many other factors on which the result, the resulting indicator, depends. Therefore, when depicting the relationship between two variables, the assumption "ceteris paribus" is used.

Like a table, a graph has a number of features or elements, the knowledge of which allows you to correctly build it manually or by machine.

The basis of any chart are:

geometric signs (points, lines, figures), with the help of which statistical values are depicted;
spatial landmarks that determine the placement of geometric symbols on the chart;
field, i.e. the place where the geometric signs are located.

Spatial landmarks are specified in the form of coordinate grids. Statistical plots usually use a rectangular coordinate system in 2D or 3D. In cartograms, the means of spatial orientation are either geographical landmarks (contours of roads, rivers, seas, forests, settlements), or administrative or state boundaries. Spatial landmarks are closely related to scale ones, which give graphic images quantitative certainty. Scale landmarks are determined by the chart scales. In this case, the scale plays the role of a conditional measure for converting quantitative values into graphic ones. In statistical graphs, as a rule, rectilinear scales are used. In this regard, the corresponding units of measurement are plotted along the abscissa and ordinate axes in conditional scales.

Curve scales are used in graphs built in the form of pie and pie charts. Both rectangular and curved scales can be uniform or non-uniform.

The field of the graph, depending on its goals and objectives, can be blank or shaded. The latter method is often used in the preparation of graphics using computer programs, which allows you to more actively highlight certain graphic images. The size of the field depends on the purpose of the chart. Like a table, a graph should have headings and verbal explanations. The name of the graph most often corresponds to the name of the table on the basis of which it is built. It must necessarily contain the names of the scales: the name of the units of measurement set aside on them (in absolute and relative numbers - in units, thousands, coefficients, percentages, etc.) and other necessary explanations. Depending on the goals of the graph, its quantitative base and the applied geometric symbols, graphs can be point (a set of points) and linear.

Line and scatter plots are the most widely used. Let's consider their use in economic analysis with an example.

Example 12.7

Let there be empirical observational data on the income of families in any region and the share of their expenditures on the purchase of non-food items during the study period (Table 12.9).

First of all, you should comprehend the data in Table. 12.9 and find out if the given dependency has economic sense. Apparently it does, since it is logical to assume that families with more high level incomes have the opportunity to spend a large share of them on the purchase of non-food products. Moreover, this situation is fully described by Engel's law, which states that as incomes rise, people spend more money on purchasing more nutritionally valuable products, and then spend more money on non-food items.

Table 12.9

Let us graphically depict how the share of family funds for the purchase of non-food items changes as their incomes grow (Fig. 12.3).

On fig. 12.3 shows that the resulting straight line is ascending. This indicates the presence of a direct relationship between the variables under consideration, i.e. these two variables change in the same direction. When there is a positive, or direct, relationship between two data series, it is always plotted as an ascending line.

The relationship between variables can be not only direct, but also reverse. For example, there is an inverse relationship between family income and the share of spending on food. If family income decreases, then the cost of purchasing food relatively increases, and vice versa, if income increases, then the share of expenses for these purposes decreases (Table 12.10).

Table 12.10

As can be seen from Table. 12.10, the variables under consideration change in opposite directions, i.e. the relationship between them is inverse or, in other words, negative.

Let's build on the basis of the data in Table. 12.10 graph (Fig. 12.4), illustrating the inverse (negative) relationship.

On fig. 12.4 it can be seen that the resulting straight line is descending. This indicates the presence of a feedback (negative) relationship between the variables under consideration, i.e. these two variables change in the same direction. When there is a negative, or inverse, relationship between two data series, it is always plotted as a descending line.

The position of a line (straight line or curve) on a graph can be characterized by the steepness of its slope and the point of intersection of this line with the y-axis or, more precisely, the axis on which the values of the dependent variable are located.

The slope of a straight line between two points is defined as the ratio of its vertical change (up or down) to the horizontal change due to movement between the points.

where ΔY is the size of the change in the dependent variable; ΔX is the size of the change in the independent variable.

Let us determine the slope of the straight line shown in Fig. 12.3. Moving from point B to point C, we can see that the increase (or vertical change characterizing the change) in the share of spending on the purchase of non-food products is + 5% (30 - 25), and the horizontal change characterizing the change in the average monthly household income is + 2500 rub. (10000 - 7500). From here:

Slope = 1% / 500 rubles.

The resulting slope of the line is positive, since the size of the average monthly family income and the share of expenditures on the purchase of non-food products change in the same direction, i.e. there is a direct, or positive, relationship between them. The + sign also indicates this.

The slope of the line at +1/500 shows that with an increase in the average monthly family income for every 500 rubles. the share of spending on the purchase of non-food items increases by 1%. Therefore, if the average monthly family income increases by 4,000 rubles, then we can assume an increase in the share of expenses associated with the purchase of non-food products by 8%. It is possible to interpret this slope in another way, based on the fact that the variables with a direct relationship change in the same direction: a decrease in the average monthly family income for every 500 rubles. entails a decrease in the share of expenditures on the purchase of non-food products by 1%. This can be seen when moving from point D to point G (Fig. 12.3). The slope of the line is:

5/-2500 = +1/500.

Consider the slope of the downward straight line. For this purpose, we use Fig. 12.4. Let's single out a fragment on it showing the relationship between changes in the average monthly family income and the share of expenses for the purchase of food products. For example, moving straight from point D to point C, one can see that the decrease or vertical change characterizing the change in the share of spending on the purchase of food products is -5% (65 - 70), and the horizontal change characterizing the change in the average monthly family income , is +2500 rubles. (12500 - 10000). From here:

Slope = -5% / +2500 rub. = -1/500.

The obtained slope of the line is negative, since the size of the average monthly family income and the share of expenses for the purchase of food products change in the opposite direction, i.e. between them there is an inverse, or negative, relationship. This is also indicated by the sign

The slope of the line at -1/500 shows that with a decrease in the average monthly family income for every 500 rubles. the share of spending on the purchase of food products increases by 1%. Therefore, if the average monthly family income decreases, for example, by 1,500 rubles, then we can assume an increase in the share of expenses associated with the purchase of food products by 3%. Increase in family income for every 500 rubles. entails a decrease in the share of expenditures on the purchase of food products by 1%.

Considering that in some cases the dependent variables are shown on the x-axis, for the correct economic interpretation of the position of the straight line on the graph, the previously given definition of the slope of the straight line should be clarified: the slope of the straight line is calculated as the ratio of the change in the dependent variable on the graph to the change in the independent variable, due to movement between points on a straight line reflecting their relationship.

Thus, the slope of the line shows us how the dependent variable responds to a certain change in the independent variable.

The slope of the line, the denominator of which is the unit value of the independent variable, shows the measure of response of the dependent variable when the independent variable changes by one unit. For example, a line slope of 1/500 can be represented (by dividing the numerator and denominator by 500) as follows: 0.002/1 or 0.002. Therefore, if the average monthly income changes by 1 rub. the share of spending on the purchase of non-food items will change in the same direction by 0.002%.

Consider the point of intersection of the straight line with the y-axis. This point shows the value of the dependent variable in the absence of any influence of the independent variable, since the value of the independent variable is equal to zero on the y-axis (y-axis).

On fig. 12.3 this point is at the 10% level (to see this, you need to extend the line to the intersection with the y-axis). This value means that if the family's income in the current month is equal to zero for some reason, then it still directs 10% of its expenses to the purchase of non-food items. It should be emphasized that Fig. 12.3 (as well as fig. 12.4) shows the dependence of the share of family expenses on the purchase of non-food (and, accordingly, food) goods on the amount of income received by the family in the current month. The possibility of acquiring non-food products is due, for example, to the use Money received in debt (credit), previously accumulated funds (savings). Neither loans nor savings can be attributed to the income of the current month.

Since at the point of intersection of a straight line (or curve) with the y-axis, the influence of the studied variable is zero, then this point shows the cumulative influence of all other factors on the studied dependent variable.

When moving along a straight line at a distance from the point of intersection with the y-axis, it can be seen that the influence of these factors on the dependent variable decreases absolutely or relatively with a simultaneous increase in the influence of the studied independent variable. Absolute decrease is typical for descending straight lines. Moreover, moving but downward straight line from top to bottom, we reach the point of its intersection with the x-axis.

At this point, as can be seen from the graph (Fig. 12.5), the value of the dependent variable is completely determined by the independent variable and the influence of other factors is zero.

On fig. 12.5 shows the dependence of the number of buyers purchasing goods in the store on the time of service of one buyer.

From fig. 12.5 it can be seen that at point A the number of buyers depends only on other factors in their totality, since the service time is zero. These factors include the number of sellers, the method of service, the area of the trading floor, etc. As you move from point A to point B, you can see that the role of these factors is decreasing, and the role of the service time factor is increasing, as the number of buyers is constantly decreasing. At point B, which lies at the intersection of the straight line with the x-axis, the number of buyers is completely determined by the service time, and the influence of all other factors is zero. From fig. Figure 12.5 shows that if the service duration is 120 minutes, customers completely refuse to make a purchase in the store, despite all the other attractive motives for them to visit this store.

Combining knowledge about the economic interpretation of the slope of a straight line and the point of intersection of a straight line with the Y axis, one can describe fig. 12.3 in the form of a mathematical equation, or, in other words, write an economic and mathematical model of the dependence of the share of expenses on the purchase of non-food products on the average monthly family income.

In general, the equation of a straight line looks like this:

where y is the dependent variable; a - the point of intersection of a straight line with the axis Y; b is the slope of the line; x is an independent variable.

In the considered in Fig. 12.3 example, y is the share of spending on the purchase of non-food items, expressed as a percentage. Parameter a is equal to 10%, parameter b is equal to +1/500, x is the average monthly family income. Let's substitute the data from Fig. 12.3 into the equation of a straight line and we get:

y \u003d 10 + 0.002x

From the resulting economic and mathematical model (equation), it can be seen that with zero income, the share of expenses for the purchase of non-food products will be 10%, and further, as the family income grows, this share will increase.

An economic-mathematical model of the dependence of the share of expenses on the purchase of food products on the average monthly family income can be written using Fig. 12.4. This model will look like this:

y \u003d 90 - 0.002x.

This model shows that at zero average monthly income, the share of family spending on the purchase of food products will be 90%, and then, as family income grows, this share will decrease in a certain proportion.

Histograms, charts and cartograms are also used to illustrate tabular information in economic analysis.

bar chart is a two-dimensional graph of the distribution of indicators. They are used to show how data has changed over a period of time, or to illustrate object comparisons. A histogram is used to display interval series. To construct a histogram based on the data of the variational series at equal intervals, the values of the argument are plotted on the abscissa axis, and the values of frequencies or relative frequencies are plotted on the ordinate axis. Next, rectangles, pyramids, cylinders are built, the bases of which are segments of the abscissa axis, the lengths of which are equal to the lengths of the intervals, and the heights are segments, the lengths of which are proportional to the frequencies or relative frequencies of the corresponding intervals.

Histograms can be flat, volumetric, cylindrical, conical, pyramidal, etc.

Diagram is a graphical representation of data that allows you to quickly evaluate the ratio of several quantities. It is a geometric symbolic representation of information using various visualization techniques. Sometimes a 3D visualization projected onto a plane is used to design diagrams, which gives the diagram a distinctive character or allows you to have a general idea of the area in which it is applied. For example, a financial chart related to amounts of money could be the number of bills in a bundle or coins in a stack; comparison diagram of the number of rolling stock - different lengths of the depicted trains, etc. Due to their clarity and ease of use, charts are often used in analytical work. Charts can be bar, bar, square, pie, surface, bubble, spade, etc.

Cartograms- these are means of visual representation of actual data that characterize individual districts, cities, regions and subjects of the federation. An example is a cartogram of sales intensity, where its level in each region has its own color or shading. Cartograms are often combined with figure charts, when certain indicators in a particular territory are indicated by figures: the sale of food products, the sale of perfumery products, etc.

Graphs that use drawings of individual objects (goods) or silhouettes (manufacturing, trading enterprises) to indicate the corresponding statistical picture are called curly.

Computer graphics makes it possible to build more complex and visual graphs and diagrams, allowing in the most concise way to clearly and intelligibly show the real state of affairs, which is more difficult to understand when studying tables or individual statistical indicators.

Questions and tasks for self-control

On what grounds are economic analysis methods classified?
List the classical methods of economic analysis.
Name non-formalized methods of economic analysis
In what case is the method of expert diagnostics used?
List the main economic and mathematical methods used in economic analysis.
How is the absolute value method used in analysis?
How is the relative value method used in analysis?
What is the purpose of using averages in analysis?
Describe the method of comparison in economic analysis.
What indicators are compared with the actual results of the enterprise?
What is the grouping method as a way of analyzing economic activity?
What is the essence index method analysis?
How to calculate the turnover (revenue) of an organization in comparable prices?
What is the essence of elimination methods?
What is the essence of the difference method?
What is the essence of the chain substitution method?
What is the essence of the balance method of economic analysis?
What is meant by independent variable?
Expand the concept of "functional cost analysis (FSA)", give examples.
What are the goals and objectives of the FSA?
Open value of the marginal analysis for a substantiation of administrative decisions.
What is the essence of margin analysis?
How can you determine the amount of conditionally fixed and variable costs?
Describe the essence of the analytical way of dividing costs into fixed and variable.

In any enterprise, all ongoing processes are interconnected. That is why economic analysis examines the degree of influence of various factors on the value. Different analytical methods of evaluation will help determine the degree of their influence: chain substitutions, the method of absolute differences, and others. In this publication, we will take a closer look at the second method.

Method of chain substitutions

This assessment option is based on the calculation of intermediate data of the indicator under study. It passes by replacing planned data with actual ones, while only one of the factors changes, the rest are excluded (the principle of elimination). Formula for calculation:

A pl \u003d a pl * b pl * c pl

A a \u003d a f * b pl * in pl

A b \u003d a f * b f * in pl

A f = a f * b f * c f

Here, the indicators according to the plan are the actual data.

Economic analysis. Absolute difference method

The considered type of evaluation is based on the previous version. The only difference is that you need to find the product of the deviation of the studied factor (D) by the planned or actual value of another. More clearly demonstrates the method of absolute differences formula:

A pl \u003d a pl * b pl * c pl

A a" \u003d a" * b pl * c pl

A b" \u003d b" * a f * in pl

A c" \u003d c" * a f * b f

A f" \u003d a f * b f * c f

A a "= A a" * A b "* A c"

Method of absolute differences. Example

The following company information is available:

the planned volume of goods produced is 1.476 million rubles, in fact - 1.428 million rubles;
the area for production according to the plan was 41 square meters. m, in fact - 42 sq. m.

It is necessary to determine how various factors (change in the size of the area and the amount of output per 1 sq. M) influenced the volume of goods created.

1) We determine the production output per 1 square. m:

1.476: 41 = 0.036 million rubles - planned value.

1.428/42 = 0.034 million rubles - actual value.

2) To solve the problem, we enter the data in the table.

Let's find the change in the volume of goods produced from the area and production, using the method of absolute differences. We get:

y a" \u003d (42 - 41) * 0.036 \u003d 0.036 million rubles.

y b" \u003d 42 * (0.034 - 0.036) \u003d - 0.084 million rubles.

The total change in the volume of production is 0.036 - 0.084 = -0.048 million rubles.

It follows that by increasing the area for production by 1 sq. m volume of manufactured goods increased by 0.036 million rubles. However, due to a decrease in production per 1 sq. m, this value decreased by 0.084 million rubles. In general, the volume of manufactured goods at the enterprise in the reporting year decreased by 0.048 million rubles.

This is how the absolute difference method works.

Relative difference method and integral

This option is used if there are relative deviations of factor values in the initial indicators, that is, in percentage terms. The formula for calculating the change in each indicator:

a%" = (a f - a pl) / a pl * 100%

b%" = (b f - b pl) / b pl * 100%

in%" = (in f - in pl) / in pl * 100%

The integral factors are based on special laws (logarithmic). The result of the calculation is determined using a PC.